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sin h AP1) Prove that lim h y Resources 1 by using only geometry. It is sufficient to consider h > 0. Hint: Use this drawing e to prove that cos 0 < sin 0 < 1 for all h-0 ourseEval 0€ (0, т/2). AP2) Prove that sin a sin y| < r - y for all x, y E R. escope AP3) Prove that f(x) = |x|x(1-x) is differentiable on R. Find all relative extrema. AP4) Prove that f(x) = |æ|x? satisfies f(0) = f'(0) =" (0) = 0, and yet f" (0) does not exist.

sin h AP1) Prove that lim h y Resources 1 by using only geometry. It is sufficient to consider h > 0. Hint: Use this drawing e to prove that cos 0 < sin 0 < 1 for all h-0 ourseEval 0€ (0, т/2). AP2) Prove that sin a sin y| < r - y for all x, y E R. escope AP3) Prove that f(x) = |x|x(1-x) is differentiable on R. Find all relative extrema. AP4) Prove that f(x) = |æ|x? satisfies f(0) = f'(0) =" (0) = 0, and yet f" (0) does not exist.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 41RE
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y Resources sin h AP1) Prove that lim sin 0 = 1 by using only geometry. It is sufficient to consider h > 0. Hint: Use this drawing e to prove that cos 0 < < 1 for all h-0 purseEval 0 E (0, 7/2). AP2) Prove that sin a – sin y|< |x – y| for all x, y E R. escope AP3) Prove that f(x) = |x|x(1-x) is differentiable on R. Find all relative extrema. AP4) Prove that f(x) = |x|x² satisfies f(0) = f'(0) =F" (0) = 0, and yet f" (0) does not exist.
Transcribed Image Text:y Resources sin h AP1) Prove that lim sin 0 = 1 by using only geometry. It is sufficient to consider h > 0. Hint: Use this drawing e to prove that cos 0 < < 1 for all h-0 purseEval 0 E (0, 7/2). AP2) Prove that sin a – sin y|< |x – y| for all x, y E R. escope AP3) Prove that f(x) = |x|x(1-x) is differentiable on R. Find all relative extrema. AP4) Prove that f(x) = |x|x² satisfies f(0) = f'(0) =F" (0) = 0, and yet f" (0) does not exist.
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